Friedrich Hasenöhrl

“ To avoid this difficulty, we want to imagine adiabatic changes of the radiation state in our cavity as of such kind, that a black body is present in the space surrounded at all sides by mirrors, yet whose capacity is so small, that its heat content can be neglected against the energy content of space . ”

“ Yet, since no work is altogether performed at uniform translation of our system, then this energy quantity must be the equivalent of a work which is performed at the acceleration of it, and which is thus added to the work against the ordinary resistance of inertia. ”

“ In § 5 the work is calculated, which must be performed to change the velocity of a cavity filled with radiation. The work that must be performed to increase the velocity, is gained again when it is decreased by the same quantity, in case the velocity change is carried out infinitively slow. ”

“ Now, when our system was initially at rest, yet the surfaces and were not hindered to emanate, then the energy density is initially present in , and it is the question, what is happening with the energy quantity when the system is suddenly brought to velocity . The previous consideration indicates that the energy amount has to be completely absorbed by the surfaces and ; no part of it may be transformed into mechanical work. ”

“ Since the heat content of every body partly consists of radiating heat, the things that we have demonstrated at a cavity, are true mutatis mutandis for every body whose temperature is different from 0° A.. ”

“ At that occasion, the work is gained from the cavity radiation again, so that no work is neither gained nor lost altogether. Yet, the density of true radiation (now the only remaining radiation in the cavity) is still equal to , though its temperature is now higher than , and thus it can by itself pass to a body whose temperature is higher than .
A new hypothesis is necessary to solve this. Such one would be the assumption, that the emission capacity of a black body changes with the velocity of translation, so that it always caeteris paribus is proportional to . ”

“ Imagine a system being at rest in the beginning, and the surfaces are somehow hindered of radiating energy, so that space contains no energy. Now, if we bring the system suddenly to velocity , and simultaneously set free the radiation of and , then the work (14) in unit time must immediately be performed against the radiation emanating from . As soon as the radiation arrives in , the same amount of work is gained there ”

“ Especially, also (16) gives the value for the pressure upon a moving mirror, when (moving in the negative or positive sense) it is hit by the total relative radiation (12a) or (12b) .
§ 3.
We now want to calculate the energy in our moving cavity. The radiation (12a) emanated from is moving with velocity according to § 1, and radiation (12b) is moving with velocity through the cavity. Since the path to be traveled by both rays in cavity is , then the time in which they are in , is equal to or ; they thus contribute the summand
to the energy content of . ”

“ Since we can also set instead of (within the expression multiplied with the infinitely small magnitude ) it eventually becomes:
Quite analogously it is given:
If we use these equations, it becomes.
or We can determine the first integral by the aid of equation (21) , the second one has the value:
thus it becomes
where is the value, which emerges from when is replaced by (see equation (21) ) . One easily convince oneself, that the bracket expression in the last equation has the value ; thus it becomes:
Our earlier assertion is proven by that. ”

“ Yet the law of reciprocity is always exactly valid for relative rays, i.e., a relative ray can always traverse the same way in both directions; this is a consequence of thermodynamics (see F. Hasenöhrl, Sitzungsber. d. k. Akad. d. Wissensch. zu Wien IIa. 113. p. 493. 1904) ↑ J. H. Poynting, Phil. Trans. ”